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3)O3–0.05BaZrO3 ceramics at microwave frequency
Materials Letters 57 (2003) 3602 – 3605 www.elsevier.com/locate/matlet
Dielectric properties of 0.95Ba(Zn1/3Nb2/3)O3 –0.05BaZrO3 ceramics at microwave frequency Cheng-Liang Huang *, Cheng-Shing Hsu, She-Jia Liu Department of Electrical Engineering, National Cheng Kung University, 1 University Road, Tainan 70101, Taiwan, ROC Received 4 October 2001; received in revised form 17 January 2003; accepted 19 January 2003
Abstract The microwave dielectric properties of conventional solid-state route prepared 0.95Ba(Zn1/3Nb2/3)O3 – 0.05BaZrO3 ceramics have been investigated. Ordering structure was not observed at sintering temperatures 1350 – 1500 jC. The dielectric constant values (er) saturated at 40 – 41. BaZrO3 was found to effectively promote the Q f value of Ba(Zn1/3Nb2/3)O3 ceramics. The Q f values of 15,000 – 96,000 (at 7 GHz) can be obtained when the sintering temperatures are in the range of 1350 – 1450 jC. The temperature coefficient of resonant frequency sf was a function of sintering temperature. The er value of 42, Q f value of 96,000 (at 7 GHz) and sf value of 27 ppm/jC were obtained for 0.95Ba(Zn1/3Nb2/3)O3 – 0.05BaZrO3 ceramics sintered at 1450 jC for 2 h. For applications of high selective microwave ceramic resonator and filter, 0.95Ba(Zn1/3Nb2/3)O3 – 0.05BaZrO3 is proposed as a suitable material candidate. D 2003 Elsevier Science B.V. All rights reserved. Keywords: Ba(Zn1/3Nb2/3)O3 – BaZrO3; Liquid phase; Microwave dielectric properties
1. Introduction The development of a microwave dielectric resonator for application in communication systems such as cellular phone, direct broadcasting satellite (DBS) and global positioning systems has been rapidly progressing in the past decade [1,2]. The advantage of using dielectric resonators is that it makes the size reduction of microwave components possible. Requirements for these dielectric resonators must be the combined dielectric properties of a high dielectric constant (er>25), a low dielectric loss ( Q>5000,
* Corresponding author. +886-6-2757575; fax: +886-62345482. E-mail address: [email protected] (C.-L. Huang).
where Q = 1/tan d) and a near-zero temperature coefficient of resonant frequency (sf) [3]. In general, high dielectric constant materials exhibit high dielectric loss (low Q f value), while low loss ceramics are always accompanied by low er value. Several complex perovskite ceramics A(B1/32 + B2/35 +)O3 have been reported due to their excellent microwave dielectric properties [4 –9]. Among these materials, Ba(Mg1/3Ta2/3)O3 possesses a very high quality factor ( Q f value f 124,000 GHz) with an er value of 23.7 at 1600 jC [8]. Onoda et al. [10] reported Ba(Zn1/3Nb2/3)O3 possessed excellent dielectric properties with a higher er value of 41. Moreover, with 5 mol% BaZrO3 replacement in Ba(Zn1/3Ta2/3) O3 ceramics, 0.95Ba(Zn1/3Ta2/3)O3 – 0.05BaZrO3 was shown to exhibit great promotion in its Q f value [11]. To develop microwave dielectric material with
0167-577X/03/$ - see front matter D 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0167-577X(03)00133-2
C.-L. Huang et al. / Materials Letters 57 (2003) 3602–3605
high dielectric constant and high Q f value, 0.95Ba (Zn1/3Nb2/3)O3 – 0.05BaZrO3 ceramics was chosen as potential candidate in this paper. Since structural ordering and disordering had been widely discussed [12 – 14], this paper would focus on the study of the microwave dielectric properties of 0.95Ba(Zn1/3Nb2/3) O3 – 0.05BaZrO3 ceramics. The XRD crystalline phases were also investigated.
2. Experimental procedures Samples of Ba(Zn1/3Nb2/3)O3 – BaZrO3 were synthesized by conventional solid-state methods from individual high-purity oxide powders (>99.9%): BaCO3, ZnO, ZrO2 and Nb2O5. The starting materials were mixed according to the desired stoichiometry of 0.95Ba(Zn1/3Nb2/3)O3 – 0.05BaZrO3 ceramics. The powders were ground in distilled water for 12 h in a ball mill with agate balls. All mixtures were dried and
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calcined at 900 jC for 2 h. The calcined reagent was ground into fine powder for 12 h. The fine powder together with the organic binder was pressed into pellets with dimensions of 11 mm in diameter and 5 mm in thickness under the pressure of 2000 kg/cm2. These pellets were sintered at temperatures of 1350 – 1500 jC for 2 h in air. The heating and the cooling rates were both set at 10 jC/min. The crystalline phases of the sintered ceramics were identified using an X-ray diffraction pattern (XRD, D5000 Diffractometer, Seimens, Germany). The bulk densities of the sintered pellets were measured by the Archimedes method. The dielectric constant (er) and the quality factor values ( Q) at microwave frequencies were measured using the Hakki– Coleman [15] dielectric resonator method as modified and improved by Courtney [16]. A system combining a HP8757D network analyzer and a HP8350B sweep oscillator was employed in the measurement. The temperature coefficient of resonant frequency (sf) at microwave fre-
Fig. 1. XRD patterns of 0.95Ba(Zn1/3Nb2/3)O3 – 0.05BaZrO3 ceramics sintered at (a) 1350 (b) 1370 (c) 1400 (d) 1425 (e) 1450 (f) 1475 and (g) 1530 jC for 2 h. (*: second phase or reflection from second phase).
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C.-L. Huang et al. / Materials Letters 57 (2003) 3602–3605
quency was measured in the temperature range from 20 to 80 jC.
3. Results and discussion Fig. 1 shows the XRD patterns of the 0.95Ba(Zn1/3 Nb2/3)O3 – 0.05BaZrO3 ceramics at different sintering temperatures for 2 h. It was observed that 0.95Ba(Zn1/3Nb2/3)O3 – 0.05BaZrO3 exhibited a disordered cubic perovskite crystal structure ( Pm3m). Similar results had been reported since ordered phases only existed for Ba(Zn1/3Nb2/3)O3 sintered at 1200 – 1300 jC for 2 h [17,18]. In addition to the main peaks, some miner peaks due to the second phase or the reflection from second phase were observed at temperatures above 1400 jC. Since it was reported that a liquid phase formed in the grain boundary accompanied by disordering for Ba(Zn1/3Nb2/3)O3 sintered above 1350 jC [18], the observed second phase was attributed to the formation of liquid phase. Furthermore, BaZrO3 seemed to inhibit the formation of liquid phase. The plot of bulk density of the 0.95Ba(Zn1/3Nb2/3) O3 –0.05BaZrO3 ceramics versus the sintering temperature is illustrated in Fig. 2. The density increased with increasing sintering temperature. After reaching a maximum at 1450 jC, it decreased. It was owing to that too high a sintering temperature would cause inhomogeneous grain growth resulting in a decrease in density. The decrease in density may directly affect the microwave dielectric properties. Fig. 3 demonstrates the dielectric constant of the 0.95Ba(Zn1/3Nb2/3)O3 – 0.05BaZrO3 ceramics as a
function of its sintering temperature. The dielectric constant revealed the same trend with the density since higher density means lower porosity results in higher er value. It increased with the increase of sintering temperature, and slightly decreased at temperatures above 1450 jC. A maximum dielectric constant was obtained for 0.95Ba(Zn1/3Nb2/3)O3 – 0.05BaZrO3 ceramics sintered at 1450 jC for 2 h. The Q f value of the 0.95Ba(Zn1/3Nb2/3)O3 – 0.05BaZrO3 ceramics as a function of it sintering temperature is illustrated in Fig. 4. The Q f value increased from 15,000 to 96,000 GHz as the sintering temperature increased from 1350 to 1450 jC. After reaching maximum at 1450 jC, it decreased. It was reported that the microwave dielectric loss was mainly caused not only by the lattice vibrational modes but also by the pores, the grain morphology and the second phases [19]. Density also plays an important role in controlling the dielectric loss and this has been shown for other microwave dielectric materials. Since
Fig. 2. The apparent density of 0.95Ba(Zn1/3Nb2/3)O3 – 0.05BaZrO3 ceramics as a function of its sintering temperature.
Fig. 4. The Q f value of 0.95Ba(Zn1/3Nb2/3)O3 – 0.05BaZrO3 ceramics as a function of its sintering temperature.
Fig. 3. The dielectric constant of 0.95Ba(Zn1/3Nb2/3)O3 – 0.05Ba ZrO3 ceramics as a function of its sintering temperature.
C.-L. Huang et al. / Materials Letters 57 (2003) 3602–3605
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value f 96,000 (at 7 GHz) and sf value f 27 ppm/ jC) can be obtained for 0.95Ba(Zn 1/3 Nb2/3)O3 – 0.05BaZrO3 sintered at 1450 jC for 2 h. For the search of high er, high Q f dielectric material, 0.95Ba(Zn1/3 Nb2/3)O3 –0.05BaZrO3 is a suitable candidate.
Acknowledgements
Fig. 5. The temperature coefficient of resonant frequency (sf) of 0.95Ba(Zn1/3Nb2/3)O3 – 0.05BaZrO3 ceramics as a function of its sintering temperature.
the Q f value revealed the same trend with the density, it implies that the variation of Q f value was dominated by the change of density. Fig. 5 shows the temperature coefficient of resonant frequency (sf) of the 0.95Ba(Zn1/3Nb2/3)O3 – 0.05BaZrO3 ceramics as a function of its sintering temperature. The sf value varied from 35 to 23.5 ppm/ jC as the sintering temperature increased from 1350 to 1500 jC. The temperature coefficient of resonant frequency (sf) is well known to be related to the composition and the second phase of a material. Since the 0.95Ba(Zn1/3Nb2/3)O3 – 0.05BaZrO3 ceramics is compositionally fixed, it is believed that liquid phase should be responsible for the variation of the sf value. At 1450 jC, a sf value of 27 ppm/jC was measured for 0.95Ba(Zn1/3Nb2/3)O3 – 0.05BaZrO3 sintered for 2 h. Two sets of samples were individually prepared to evaluate the reproducibility. Variations of measured data were less than 3% for the entire experiment.
4. Conclusion The microwave dielectric properties of the 0.95 Ba(Zn1/3Nb2/3)O3 –0.05BaZrO3 ceramics were investigated. The ceramics exhibited a disordered cubic perovskite crystal structure at 1350 –1500 jC. Liquid phase appeared at temperatures above 1400 jC. Excellent microwave dielectric properties (er ~42, Q f
This work was co-supported by the National Science Council of the Republic of China under grant NSC90-2213-E-006-061 and the Foundation of JiehChen Chen Scholarship, Tainan, Taiwan.
References [1] S. Nishigaki, H. Kato, S. Yano, R. Kamimure, Am. Ceram. Soc. Bull. 66 (1987) 1405. [2] K. Wakino, K. Minai, H. Tamura, J. Am. Ceram. Soc. 67 (1984) 278. [3] T. Takada, S.F. Wang, S. Yoshikawa, S.J. Yang, R.E. Newnham, J. Am. Ceram. Soc. 77 (1994) 1909. [4] S. Kawashima, M. Nishida, I. Ueda, H. Ouchi, J. Am. Ceram. Soc. 66 (1983) 421. [5] K. Endo, K. Fujimoto, K. Murakawa, J. Am. Ceram. Soc. 70 (1987) C215. [6] H. Matsumoto, H. Tamura, K. Wakino, Jpn. J. Appl. Phys. 30 (1991) 2347. [7] K.H. Yoon, D.P. Kim, E.S. Kim, J. Am. Ceram. Soc. 77 (1994) 1062. [8] H.J. Youn, K.K. Kim, H. Kim, Jpn. J. Appl. Phys. 35 (1996) 3947. [9] S. Nomura, K. Toyama, K. Kaneta, Jpn. J. Appl. Phys. 21 (1982) L624. [10] M. Onoda, K. Kuwata, K. Kaneta, K. Toyama, S. Nomura, Jpn. J. Appl. Phys. 21 (1982) 1707. [11] H. Tamura, T. Konoike, Y. Sakabe, K. Wakino, Comm. Am. Ceram. Soc (1984) C-59. [12] J. Barber, K.M. Moulding, J. Zhou, J. Mater. Sci. 32 (1997) 1531. [13] M.A. Akbas, P.K. Davies, J. Am. Ceram. Soc. 81 (1998) 1061. [14] L. Chai, P.K. Davies, J. Am. Ceram. Soc. 80 (1997) 3193. [15] B.W. Hakki, P.D. Coleman, IEEE Trans. Microwave Theor. Tech. 8 (1960) 402. [16] W.E. Courtney, IEEE Trans. Microwave Theor. Tech. 18 (1970) 476. [17] B.-K. Kim, H. Hamaguchi, I.-T. Kim, K.S. Hong, J. Am. Ceram. Soc. 78 (1995) 3117. [18] K.S. Hong, J. Am. Ceram. Soc. 79 (1996) 3218. [19] B.D. Silverman, Phys. Rev. 125 (1962) 1921.
Dielectric properties of 0.95Ba(Zn1/3Nb2/3)O3 –0.05BaZrO3 ceramics at microwave frequency Cheng-Liang Huang *, Cheng-Shing Hsu, She-Jia Liu Department of Electrical Engineering, National Cheng Kung University, 1 University Road, Tainan 70101, Taiwan, ROC Received 4 October 2001; received in revised form 17 January 2003; accepted 19 January 2003
Abstract The microwave dielectric properties of conventional solid-state route prepared 0.95Ba(Zn1/3Nb2/3)O3 – 0.05BaZrO3 ceramics have been investigated. Ordering structure was not observed at sintering temperatures 1350 – 1500 jC. The dielectric constant values (er) saturated at 40 – 41. BaZrO3 was found to effectively promote the Q f value of Ba(Zn1/3Nb2/3)O3 ceramics. The Q f values of 15,000 – 96,000 (at 7 GHz) can be obtained when the sintering temperatures are in the range of 1350 – 1450 jC. The temperature coefficient of resonant frequency sf was a function of sintering temperature. The er value of 42, Q f value of 96,000 (at 7 GHz) and sf value of 27 ppm/jC were obtained for 0.95Ba(Zn1/3Nb2/3)O3 – 0.05BaZrO3 ceramics sintered at 1450 jC for 2 h. For applications of high selective microwave ceramic resonator and filter, 0.95Ba(Zn1/3Nb2/3)O3 – 0.05BaZrO3 is proposed as a suitable material candidate. D 2003 Elsevier Science B.V. All rights reserved. Keywords: Ba(Zn1/3Nb2/3)O3 – BaZrO3; Liquid phase; Microwave dielectric properties
1. Introduction The development of a microwave dielectric resonator for application in communication systems such as cellular phone, direct broadcasting satellite (DBS) and global positioning systems has been rapidly progressing in the past decade [1,2]. The advantage of using dielectric resonators is that it makes the size reduction of microwave components possible. Requirements for these dielectric resonators must be the combined dielectric properties of a high dielectric constant (er>25), a low dielectric loss ( Q>5000,
* Corresponding author. +886-6-2757575; fax: +886-62345482. E-mail address: [email protected] (C.-L. Huang).
where Q = 1/tan d) and a near-zero temperature coefficient of resonant frequency (sf) [3]. In general, high dielectric constant materials exhibit high dielectric loss (low Q f value), while low loss ceramics are always accompanied by low er value. Several complex perovskite ceramics A(B1/32 + B2/35 +)O3 have been reported due to their excellent microwave dielectric properties [4 –9]. Among these materials, Ba(Mg1/3Ta2/3)O3 possesses a very high quality factor ( Q f value f 124,000 GHz) with an er value of 23.7 at 1600 jC [8]. Onoda et al. [10] reported Ba(Zn1/3Nb2/3)O3 possessed excellent dielectric properties with a higher er value of 41. Moreover, with 5 mol% BaZrO3 replacement in Ba(Zn1/3Ta2/3) O3 ceramics, 0.95Ba(Zn1/3Ta2/3)O3 – 0.05BaZrO3 was shown to exhibit great promotion in its Q f value [11]. To develop microwave dielectric material with
0167-577X/03/$ - see front matter D 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0167-577X(03)00133-2
C.-L. Huang et al. / Materials Letters 57 (2003) 3602–3605
high dielectric constant and high Q f value, 0.95Ba (Zn1/3Nb2/3)O3 – 0.05BaZrO3 ceramics was chosen as potential candidate in this paper. Since structural ordering and disordering had been widely discussed [12 – 14], this paper would focus on the study of the microwave dielectric properties of 0.95Ba(Zn1/3Nb2/3) O3 – 0.05BaZrO3 ceramics. The XRD crystalline phases were also investigated.
2. Experimental procedures Samples of Ba(Zn1/3Nb2/3)O3 – BaZrO3 were synthesized by conventional solid-state methods from individual high-purity oxide powders (>99.9%): BaCO3, ZnO, ZrO2 and Nb2O5. The starting materials were mixed according to the desired stoichiometry of 0.95Ba(Zn1/3Nb2/3)O3 – 0.05BaZrO3 ceramics. The powders were ground in distilled water for 12 h in a ball mill with agate balls. All mixtures were dried and
3603
calcined at 900 jC for 2 h. The calcined reagent was ground into fine powder for 12 h. The fine powder together with the organic binder was pressed into pellets with dimensions of 11 mm in diameter and 5 mm in thickness under the pressure of 2000 kg/cm2. These pellets were sintered at temperatures of 1350 – 1500 jC for 2 h in air. The heating and the cooling rates were both set at 10 jC/min. The crystalline phases of the sintered ceramics were identified using an X-ray diffraction pattern (XRD, D5000 Diffractometer, Seimens, Germany). The bulk densities of the sintered pellets were measured by the Archimedes method. The dielectric constant (er) and the quality factor values ( Q) at microwave frequencies were measured using the Hakki– Coleman [15] dielectric resonator method as modified and improved by Courtney [16]. A system combining a HP8757D network analyzer and a HP8350B sweep oscillator was employed in the measurement. The temperature coefficient of resonant frequency (sf) at microwave fre-
Fig. 1. XRD patterns of 0.95Ba(Zn1/3Nb2/3)O3 – 0.05BaZrO3 ceramics sintered at (a) 1350 (b) 1370 (c) 1400 (d) 1425 (e) 1450 (f) 1475 and (g) 1530 jC for 2 h. (*: second phase or reflection from second phase).
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C.-L. Huang et al. / Materials Letters 57 (2003) 3602–3605
quency was measured in the temperature range from 20 to 80 jC.
3. Results and discussion Fig. 1 shows the XRD patterns of the 0.95Ba(Zn1/3 Nb2/3)O3 – 0.05BaZrO3 ceramics at different sintering temperatures for 2 h. It was observed that 0.95Ba(Zn1/3Nb2/3)O3 – 0.05BaZrO3 exhibited a disordered cubic perovskite crystal structure ( Pm3m). Similar results had been reported since ordered phases only existed for Ba(Zn1/3Nb2/3)O3 sintered at 1200 – 1300 jC for 2 h [17,18]. In addition to the main peaks, some miner peaks due to the second phase or the reflection from second phase were observed at temperatures above 1400 jC. Since it was reported that a liquid phase formed in the grain boundary accompanied by disordering for Ba(Zn1/3Nb2/3)O3 sintered above 1350 jC [18], the observed second phase was attributed to the formation of liquid phase. Furthermore, BaZrO3 seemed to inhibit the formation of liquid phase. The plot of bulk density of the 0.95Ba(Zn1/3Nb2/3) O3 –0.05BaZrO3 ceramics versus the sintering temperature is illustrated in Fig. 2. The density increased with increasing sintering temperature. After reaching a maximum at 1450 jC, it decreased. It was owing to that too high a sintering temperature would cause inhomogeneous grain growth resulting in a decrease in density. The decrease in density may directly affect the microwave dielectric properties. Fig. 3 demonstrates the dielectric constant of the 0.95Ba(Zn1/3Nb2/3)O3 – 0.05BaZrO3 ceramics as a
function of its sintering temperature. The dielectric constant revealed the same trend with the density since higher density means lower porosity results in higher er value. It increased with the increase of sintering temperature, and slightly decreased at temperatures above 1450 jC. A maximum dielectric constant was obtained for 0.95Ba(Zn1/3Nb2/3)O3 – 0.05BaZrO3 ceramics sintered at 1450 jC for 2 h. The Q f value of the 0.95Ba(Zn1/3Nb2/3)O3 – 0.05BaZrO3 ceramics as a function of it sintering temperature is illustrated in Fig. 4. The Q f value increased from 15,000 to 96,000 GHz as the sintering temperature increased from 1350 to 1450 jC. After reaching maximum at 1450 jC, it decreased. It was reported that the microwave dielectric loss was mainly caused not only by the lattice vibrational modes but also by the pores, the grain morphology and the second phases [19]. Density also plays an important role in controlling the dielectric loss and this has been shown for other microwave dielectric materials. Since
Fig. 2. The apparent density of 0.95Ba(Zn1/3Nb2/3)O3 – 0.05BaZrO3 ceramics as a function of its sintering temperature.
Fig. 4. The Q f value of 0.95Ba(Zn1/3Nb2/3)O3 – 0.05BaZrO3 ceramics as a function of its sintering temperature.
Fig. 3. The dielectric constant of 0.95Ba(Zn1/3Nb2/3)O3 – 0.05Ba ZrO3 ceramics as a function of its sintering temperature.
C.-L. Huang et al. / Materials Letters 57 (2003) 3602–3605
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value f 96,000 (at 7 GHz) and sf value f 27 ppm/ jC) can be obtained for 0.95Ba(Zn 1/3 Nb2/3)O3 – 0.05BaZrO3 sintered at 1450 jC for 2 h. For the search of high er, high Q f dielectric material, 0.95Ba(Zn1/3 Nb2/3)O3 –0.05BaZrO3 is a suitable candidate.
Acknowledgements
Fig. 5. The temperature coefficient of resonant frequency (sf) of 0.95Ba(Zn1/3Nb2/3)O3 – 0.05BaZrO3 ceramics as a function of its sintering temperature.
the Q f value revealed the same trend with the density, it implies that the variation of Q f value was dominated by the change of density. Fig. 5 shows the temperature coefficient of resonant frequency (sf) of the 0.95Ba(Zn1/3Nb2/3)O3 – 0.05BaZrO3 ceramics as a function of its sintering temperature. The sf value varied from 35 to 23.5 ppm/ jC as the sintering temperature increased from 1350 to 1500 jC. The temperature coefficient of resonant frequency (sf) is well known to be related to the composition and the second phase of a material. Since the 0.95Ba(Zn1/3Nb2/3)O3 – 0.05BaZrO3 ceramics is compositionally fixed, it is believed that liquid phase should be responsible for the variation of the sf value. At 1450 jC, a sf value of 27 ppm/jC was measured for 0.95Ba(Zn1/3Nb2/3)O3 – 0.05BaZrO3 sintered for 2 h. Two sets of samples were individually prepared to evaluate the reproducibility. Variations of measured data were less than 3% for the entire experiment.
4. Conclusion The microwave dielectric properties of the 0.95 Ba(Zn1/3Nb2/3)O3 –0.05BaZrO3 ceramics were investigated. The ceramics exhibited a disordered cubic perovskite crystal structure at 1350 –1500 jC. Liquid phase appeared at temperatures above 1400 jC. Excellent microwave dielectric properties (er ~42, Q f
This work was co-supported by the National Science Council of the Republic of China under grant NSC90-2213-E-006-061 and the Foundation of JiehChen Chen Scholarship, Tainan, Taiwan.
References [1] S. Nishigaki, H. Kato, S. Yano, R. Kamimure, Am. Ceram. Soc. Bull. 66 (1987) 1405. [2] K. Wakino, K. Minai, H. Tamura, J. Am. Ceram. Soc. 67 (1984) 278. [3] T. Takada, S.F. Wang, S. Yoshikawa, S.J. Yang, R.E. Newnham, J. Am. Ceram. Soc. 77 (1994) 1909. [4] S. Kawashima, M. Nishida, I. Ueda, H. Ouchi, J. Am. Ceram. Soc. 66 (1983) 421. [5] K. Endo, K. Fujimoto, K. Murakawa, J. Am. Ceram. Soc. 70 (1987) C215. [6] H. Matsumoto, H. Tamura, K. Wakino, Jpn. J. Appl. Phys. 30 (1991) 2347. [7] K.H. Yoon, D.P. Kim, E.S. Kim, J. Am. Ceram. Soc. 77 (1994) 1062. [8] H.J. Youn, K.K. Kim, H. Kim, Jpn. J. Appl. Phys. 35 (1996) 3947. [9] S. Nomura, K. Toyama, K. Kaneta, Jpn. J. Appl. Phys. 21 (1982) L624. [10] M. Onoda, K. Kuwata, K. Kaneta, K. Toyama, S. Nomura, Jpn. J. Appl. Phys. 21 (1982) 1707. [11] H. Tamura, T. Konoike, Y. Sakabe, K. Wakino, Comm. Am. Ceram. Soc (1984) C-59. [12] J. Barber, K.M. Moulding, J. Zhou, J. Mater. Sci. 32 (1997) 1531. [13] M.A. Akbas, P.K. Davies, J. Am. Ceram. Soc. 81 (1998) 1061. [14] L. Chai, P.K. Davies, J. Am. Ceram. Soc. 80 (1997) 3193. [15] B.W. Hakki, P.D. Coleman, IEEE Trans. Microwave Theor. Tech. 8 (1960) 402. [16] W.E. Courtney, IEEE Trans. Microwave Theor. Tech. 18 (1970) 476. [17] B.-K. Kim, H. Hamaguchi, I.-T. Kim, K.S. Hong, J. Am. Ceram. Soc. 78 (1995) 3117. [18] K.S. Hong, J. Am. Ceram. Soc. 79 (1996) 3218. [19] B.D. Silverman, Phys. Rev. 125 (1962) 1921.